Simplify the following expression: $r = \dfrac{-3n^2 - 33n - 72}{n + 3} $
First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-3$ , so we can rewrite the expression: $ r =\dfrac{-3(n^2 + 11n + 24)}{n + 3} $ Then we factor the remaining polynomial: $n^2 + {11}n + {24} $ ${3} + {8} = {11}$ ${3} \times {8} = {24}$ $ (n + {3}) (n + {8}) $ This gives us a factored expression: $\dfrac{-3(n + {3}) (n + {8})}{n + 3}$ We can divide the numerator and denominator by $(n - 3)$ on condition that $n \neq -3$ Therefore $r = -3(n + 8); n \neq -3$